Amembrane that allows only some materials to move in and out of the cell is permeable semipermeable rigid bilayered

A membrane that allows only some materials to move in and out of the cell is semi permeable. A semipermeable membrane is a type of biological or artificial membrane that allows certain molecules or ions to move in and out of it by diffusion. The rate of passage depends on the permeability of the membrane to each solute and the pressure, concentration, and temperature of the molecules or solutes on each side.

the answer is semipermeable membrane. as the name suggests this membrane only allows certain molecules to pass in and out of the cell. Its selective in the materials that are allowed to pass through the membrane . While it allows water molecules to pass through the membrane other ions and molecules are selectively allowed.